Vibration Signal Frequency Domain Analysis and Fault Diagnosis

# 1. Basic Knowledge of Vibration Signals

Vibration signals are a common type of signal found in the field of engineering, containing information generated by objects as they vibrate. Vibration signals can be captured by sensors and analyzed through specific processing techniques. In fault diagnosis, the analysis of vibration signals plays a crucial role.

#### 1.1 Overview of Vibration Signals

A vibration signal refers to the signal generated by an object during its vibrational process, typically containing information such as amplitude, frequency, and phase. Vibration signals can be used to determine the operating state of an object, its structural characteristics, and any potential fault information.

#### 1.2 Collection and Processing Techniques for Vibration Signals

The collection of vibration signals is usually done using accelerometers or vibration sensors, and the signals obtained need to be processed through filtering, amplification, sampling, etc., to obtain accurate vibration information.

#### 1.3 The Importance of Vibration Signals in Fault Diagnosis

Vibration signals contain dynamic information about objects as they vibrate. By analyzing vibration signals, one can determine whether there are abnormal vibrations or potential faults in the object, allowing for timely maintenance and care, thereby improving the reliability and safety of the equipment.

# 2. Basics of Frequency Domain Analysis

In the context of vibration signal frequency domain analysis and fault diagnosis, frequency domain analysis is an important tool and method. This chapter will introduce the basic knowledge of frequency domain analysis, including the concept of signal frequency domain representation, Fourier Transform and spectral analysis, and commonly used tools and methods for frequency domain analysis.

#### 2.1 Concept of Signal Frequency Domain Representation

In signal processing, time domain analysis and frequency domain analysis are two commonly used methods. Time domain representation shows how signals change over time, while frequency domain representation shows the characteristics of signals in terms of frequency. Frequency domain analysis can display the components of a signal in terms of frequency, thereby better understanding the characteristics and properties of the signal.

#### 2.2 Fourier Transform and Spectral Analysis

The Fourier Transform is an important mathematical tool for converting signals from the time domain to the frequency domain. Through the Fourier Transform, signals can be represented as a superposition of sine and cosine waves of different frequencies. Spectral analysis is the process of analyzing and displaying the characteristics of signals in the frequency domain, with common methods including power spectral density analysis and spectral plot drawing.

#### 2.3 Common Tools and Methods for Frequency Domain Analysis

In frequency domain analysis, common tools and methods include the Fast Fourier Transform (FFT), power spectral density analysis, and spectral plot drawing. These tools and methods help engineers and researchers better understand the characteristics of vibration signals in the frequency domain, thereby providing support and guidance for fault diagnosis.

# 3. Feature Analysis of Vibration Signals in the Frequency Domain

Feature analysis of vibration signals in the frequency domain is crucial for fault diagnosis. By extracting and analyzing the spectral features of vibration signals, one can more accurately identify whether there are faults in the equipment and further analyze the type and cause of the faults.

#### 3.1 Extraction of Vibration Signal Spectral Feature Parameters

In frequency domain analysis, the spec***mon spectral feature parameters include, but are not limited to:

- Peak Frequency: The frequency corresponding to the highest energy in the signal spectrum.
- Peak-to-Peak Frequency: The frequency range between two energy peaks in the signal spectrum.
- Spectrum Width: The width of the spectral energy distribution, used to determine the shape of the signal spectrum.
- Spectrum Crest Factor: The ratio of the spectral peak to the mean, reflecting the degree of signal peaking.
- Spectrum Skewness: Reflects the degree of skewness in the spectral energy distribution.

By extracting these spectral feature parameters, one can comprehensively understand the frequency domain characteristics of vibration signals from different perspectives, providing a basis for subsequent fault diagnosis.

#### 3.2 Interpretation and Diagnosis of Vibration Signal Frequency Domain Plots

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